Multi-step method for determining the energy spectrum of different quantum potential wells
DOI:
https://doi.org/10.19136/jobs.a10n29.5033Keywords:
Multi-step, Potential well, Schrödinger equation, Bound states, MOSFETAbstract
In this work, the bound states of a quantum system with a triangular potential well are numerically determined. Additionally, a practical case is studied in which a potential found in MOSFET devices is analyzed. In both cases, the multi-step approximation method is used, which involves approximating the potential by a chain of n-step potentials. From this new potential, the expressions for the reflection and transmission coefficients are determined through a recursive formula, which is a generalization of the coefficients for the simple step potential case. For the system with a triangular well, two bound energies are found with relative errors of less than 1%, while for the potential associated with MOSFET devices, only one bound energy is obtained
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